Rate of reaction in detector?

A reactor fires out ##10^{21}## neutrinos per second. A detector containing ##10m^3## of liquid which contains 30 carbon atoms every 60 hydrogen atoms. The detector-reactor distance is ##1000##. The cross section for the reaction is ##\sigma = 10^{-46} m^2##, and the density of the liquid is ##870 kg m^{-3}##. Find the expected rate of reactions.

2. Relevant equations

3. The attempt at a solution

I know that the rate of reactions is ##W = \sigma J n \delta x## where ##J## is incoming particles per second and ##n## is number density and ##\delta x## is thickness.
Number of carbon atoms per unit volume in the detector is ##\frac{60}{90} \frac{(870)(10.3)}{(1.67 \times 10^{-27}) (10.3)} = 3.5 \times 10^{29} m^{-3}##. Can I take ##J## to be ##10^{21}##? What is the thickness in this case?